This invention relates to an apparatus for X-ray analysis which uses a composite monochromator having combined two elliptic monochromators, the composite monochromator being arranged between an X-ray source and a sample.
In the field of X-ray analysis, there has always been required to make the X-ray intensity as high as possible. A stationary-anode X-ray tube (e.g., 0.4 mm.times.12 mm in focal spot size and 2.2 kW in maximum power) has a limit for increasing the X-ray intensity. To overcome this limitation, a rotating-anode X-ray tube which provides a higher X-ray intensity has been developed and used. There has also been used synchrotron radiation which provides a much higher X-ray intensity. The X-ray generator having such a higher X-ray intensity, however, is big and complicated in handling, and further spends much energy. Under the circumstances, there is more and more of a need to develop an apparatus for X-ray analysis which can increase the X-ray intensity on a sample even though it can be handled easily in laboratories.
Assuming that a sample is set at a distance of several hundred millimeters apart from an X-ray source and an X-ray beam is incident on the sample directly from the X-ray source, the sample receives only a very small percentage of the X-rays which are emitted in all directions from the focal spot on the target of the X-ray source. Accordingly, it is known that optical elements such as mirrors or monochromators are used to focus X-rays on the sample. Persons in the art have sought for an improved focusing efficiency of such an X-ray optical system to save energy further.
Elliptic or parabolic focusing elements with a synthetic multilayered thin film have recently been developed and given attention by persons in the field of X-ray analysis, the elements having high focusing efficiencies and high reflectivity for X-rays of a predetermined wavelength of interest. The focusing elements of this type are disclosed, for example, in U.S. Pat. Nos. 5,799,056; 5,757,882; 5,646,976; and 4,525,853; and M. Schuster and H. Gobel, "Parallel-Beam Coupling into Channel-Cut Monochromators Using Curved Graded Multilayers", J. Phys. D: Appl. Phys. 28(1995)A270-A275, Printed in the UK; G. Gutman and B. Verman, "Comment, Calculation of Improvement to HRXRD System Through-Put Using Curved Graded Multilayers", J. Phys. D: Appl. Phys. 29(1996)1675-1676, Printed in the UK; and M. Schuster and H. Gobel, "Reply to Comment, Calculation of Improvement to HRXRD System Through-Put Using Curved Graded Multilayers", J. Phys. D: Appl. Phys. 29(1996)1677-1679, Printed in the UK. There are further disclosed structures of the synthetic multilayered thin film for X-ray reflection and methods for producing them, for example, in Japanese Patent Post-Exam Publication No. 94/46240 and U.S. Patent No. 4,693,933.
The synthetic multilayered thin film acts as a focusing monochromator for X-rays. It is certain that a combination of an ordinary X-ray source and the above focusing-type synthetic multilayered thin film may greatly increase the X-ray intensity on a sample.
There will now be described with reference to FIGS. 5 to 12 the shape, structure and function of the prior-art elliptic monochromator having the synthetic multilayered thin film. First, the meaning of the terms "elliptic monochromator", "elliptic-arc surface" and "focal axis" will be described. Referring to FIG. 5, a three-dimensional rectangular coordinate axis XYZ is set in space and an ellipse 10 is drawn in an XY-plane. Imagining a curve 12 which is a portion of the ellipse 10, the curve 12 is referred to hereinafter as "elliptic-arc". The elliptic-arc 12 is translated in the Z-direction (i.e., the direction perpendicular to the plane including the elliptic-arc 12) to make a trace which becomes a curved surface 14. The curved surface 14 is referred to hereinafter as "elliptic-arc surface". The two foci F.sub.1 and F.sub.2 of the elliptic-arc surface 12 are translated in the Z-direction to make two traces 20 and 22 each of which is referred to hereinafter as "focal axis". The focal axes 20 and 22 of the elliptic-arc surface 14 become parallel to the Z-axis. A normal line drawn at any point on the elliptic-arc surface 14 becomes always parallel to the XY-plane. Under the above positional relationship, the elliptic-arc surface 14 can be represented by "elliptic-arc surface with focal axes parallel to the Z-axis". It should be noted that the monochromator whose reflecting surface consists of an elliptic-arc surface is referred to simply as "elliptic monochromator".
Next, the function of the elliptic monochromator will be described. Referring to FIG. 6, imagine an elliptic monochromator 24 with focal axes parallel to the X-axis. The drawing sheet of FIG. 6 is parallel to the YZ-plane. The reflecting surface 26 of the elliptic monochromator 24 appears as an elliptic-arc on the drawing sheet of FIG. 6. In view of geometrical optics, a light ray emitted from a light source, which is positioned at one focal point F.sub.1 of the elliptic-arc, is reflected at the reflecting surface 26 and reach the other focal point F.sub.2.
In view of X-ray optics, an X-ray emitted from an X-ray source, which is positioned at one focal point F.sub.1, may be reflected at the reflecting surface 26 only when an X-ray incidence angle .theta. on the reflecting surface 26, an X-ray wavelength .lambda. and the lattice spacing d of crystal of the reflecting surface 26 satisfy the Bragg equation for diffraction. The reflected X-ray will reach the other focal point F.sub.2. It should be noted that the lattice surfaces of crystal contributing to the diffraction are parallel to the reflecting surface 26.
Incidentally, the X-ray incidence angle .theta. on the reflecting surface 26 depends upon the position, on which an X-ray is incident, of the reflecting surface 26 of the elliptic monochromator 24. Therefore, to satisfy the Bragg equation at any point of the reflecting surface 26, the lattice spacing must be graded along the elliptic-arc (i.e., must vary with the incidence angle .theta.). The elliptic monochromator for X-rays has accordingly a synthetic multilayered thin film in which the d-spacing of the multilayers varies continuously. The d-spacing varying continuously is referred to hereinafter as graded d-spacing.
FIG. 7 shows the functional principle of the elliptic monochromator having graded d-spacing. X-rays emitted from the X-ray source 32 are incident on a point A, having d-spacing d.sub.1, of the reflecting surface 26 of the elliptic monochromator 24 with an incidence angle .theta..sub.1 and on a point B having d-spacing d.sub.2 with an incidence angle .theta..sub.2. The Bragg equation at the point A is EQU 2d.sub.1 sin.theta..sub.1 =.lambda. (1)
where .lambda. is the wavelength of the X-rays. The Bragg equation at the point B is EQU 2d.sub.2 sin.theta..sub.2 =.lambda.. (2)
If the positional relationship between the X-ray source 32 and the elliptic monochromator 24 is predetermined, the incidence angle .theta. could be calculated at any point of the reflecting surface 26 of the elliptic monochromator 24, and accordingly the d-spacing for every incidence angle .theta. could also be calculated so as to satisfy the Bragg equation.
With the use of such an elliptic monochromator having the graded d-spacing, X-rays of a particular wavelength of interest always satisfy the Bragg equation even if the X-rays are incident on any point of the reflecting surface, so that the reflected X-rays of the particular wavelength can be focused at the other focal point F.sub.2. The elliptic monochromator having such a synthetic multilayered thin film per se is known as mentioned above.
Referring to FIG. 6, X-rays, emitted from the focal point F.sub.1 and traveling in the direction within a divergence angle .alpha., are reflected by the reflecting surface 26 of the elliptic monochromator 26 and focused on the other focal point F.sub.2 with a convergence angle .beta.. With such a focusing effect, X-rays with the predetermined divergence angle can be utilized effectively, so that the X-ray intensity on the focal point F.sub.2 may be greatly increased as compared with the case of no elliptic monochromator. At the same time, X-rays may be purified into the specific monochromatic rays with the function of the elliptic monochromator 24.
While we have considered, with reference to FIG. 6, the focusing of the X-rays which diverge in the XY-plane, the focusing of the X-rays which diverge in the ZX-plane can be realized when we use an "elliptic monochromator with focal axes parallel to the Y-axis". Accordingly, if both the "elliptic monochromator with focal axes parallel to the X-axis" and the "elliptic monochromator with focal axes parallel to the Y-axis" are arranged between the X-ray source and the sample, the focusing for both the divergence in the YZ-plane and the divergence in the ZX-plane can be realized. Under such an arrangement, the X-ray source must be positioned on one focal point of the "elliptic monochromator with focal axes parallel to the X-axis" and at the same time on one focal point of the "elliptic monochromator with focal axes parallel to the Y-axis" too.
One arrangement of the elliptic monochromator system which can focus X-rays in both the YZ-plane and the ZX-plane may be a sequential arrangement as shown in FIG. 8A. This arrangement is disclosed in by V. E. Cosslett and W. C. Nixon, "X-ray Microscopy", Cambridge at the University Press, 1960, pp.105-109. Referring to FIG. 8A, X-rays emitted from an X-ray source 32 are reflected first at the first elliptic monochromator 34 (the elliptic monochromator with focal axes parallel to the X-axis) so that the divergence in the YZ-plane is focused. The X-rays are reflected next at the second elliptic monochromator 36 (the elliptic monochromator with focal axes parallel to the Y-axis) so that the divergence in the ZX-plane is focused.
Another arrangement is a side-by-side arrangement as shown in FIG. 8B and this arrangement is disclosed in S. Flugge, "Encyclopedia of Physics", Volume XXX, X-rays, Springer-Verlag, Berlin.cndot.Gottingen.cndot.Heidelberg, 1957, pp.324-32. The side-by-side elliptic monochromator system has the first elliptic monochromator 38 (the elliptic monochromator with focal axes parallel to the X-axis) and the second elliptic monochromator 40 (the elliptic monochromator with focal axes parallel to the Y-axis), these monochromators being so combined that one side of the first monochromator 38 is in contact with one side of the second monochromator 40. X-rays emitted from an X-ray source 32 are reflected first at either one of the first elliptic monochromator 38 and the second elliptic monochromator 40, and further reflected, soon after the first reflection, at the other monochromator, so that the X-rays are focused on a convergence point 44. X-rays emitted from the X-ray source 32 must first impinge on the region 42 as indicated by hatching for enabling the sequential reflection on the two elliptic monochromators 38 and 40. Thus, the side-by-side composite monochromator utilizes the sequential reflection at the region 42 near the corner between the two monochromators.
FIG. 9A is a view taken in the X-direction of FIG. 8B, and FIG. 9B is a view taken in the Y-direction of FIG. 8B. In FIGS. 9A and 9B, X-rays emitted from the X-ray source 32 are reflected first at a point C on the reflecting surface of the first elliptic monochromator 38 and reflected next at a point D on the reflecting surface of the second elliptic monochromator 40, so that the X-rays are focused on the convergence point 44.
In another route as shown in FIGS. 10A and 10B, X-rays emitted from the X-ray source 32 are reflected first at a point E on the reflecting surface of the second elliptic monochromator 40 and reflected next at a point F on the reflecting surface of the first elliptic monochromator 38, so that the X-rays are focused on the convergence point 44.
Referring back to FIG. 8B, when seen in the X-direction, the X-ray source 32 is positioned at one focal point of the first elliptic monochromator 38, while the convergence point 44 is on the other focal point. On the other hand, when seen in the Y-direction, the X-ray source 32 is positioned at one focal point of the second elliptic monochromator 40, while the convergence point 44 is on the other focal point.
By the way, in FIG. 8B, when X-rays are incident first on any point which is out of the hatching region 42, the reflected X-rays from that point do not impinge on the other elliptic monochromator any longer. Such X-rays can not reach the convergence point 44. Stating in detail, when X-rays are incident first on any point, on the reflecting surface of the first elliptic monochromator 38, which is out of the region 42, the reflected X-rays from that point are focused on a line 46 (parallel to the X-axis). On the other hand, when X-rays are incident first on any point, on the reflecting surface of the second elliptic monochromator 40, which is out of the region 42, the reflected X-rays from that point are focused on a line 48 (parallel to the Y-axis). It is noted that the convergence point 44 is located at the intersection of an extension of the line 46 and an extension of the line 48. If a sample is set on the convergence point 44, only X-rays which are focused in both the YZ-plane and the ZX-plane may irradiate the sample.
With the sequential-type composite monochromator as shown in FIG. 8A, a divergence angle, with which X-rays are caught by the composite monochromator, in the YZ-plane is different from a divergence angle in the ZX-plane. On the contrary, with the side-by-side composite monochromator as shown in FIG. 8B, a divergence angle, with which X-rays are caught by the composite monochromator, in the YZ-plane is equal to a divergence angle in the ZX-plane because the distances between the X-ray source 32 and the two monochromators 38 and 40 are equal to each other.
Referring to FIG. 11 which illustrates an effect of the focal spot size of an X-ray source, when an X-ray source 32 is positioned at one focal point of the reflecting surface of an elliptic monochromator 24, X-rays emitted from the X-ray source 32 are incident on a point A on the reflecting surface of the elliptic monochromator 24 with an incidence angle .theta.. The incidence angle .theta. depends upon where the X-rays impinge on along the elliptic-arc of the reflecting surface of the elliptic monochromator 24. Because the elliptic monochromator 24 has the graded d-spacing along the curve, the d-spacing, the X-ray wavelength .lambda. of interest and the incidence angle .theta. at any point A satisfy the Bragg equation as described above. By the way, the X-ray source 32 has an apparent focal spot size D as viewed from the point A, and accordingly the incidence angle .theta. at the point A has an angular width .DELTA..theta. (breadth of incidence angle) of a certain extent. As to the breadth .DELTA..theta. the following equation (3) is obtained: EQU D/2=S.multidot.sin(.DELTA..theta./2) (3)
where S is the distance between the X-ray source 32 and the point A, and D is the apparent focal spot size of the X-ray source 32. Because .DELTA..theta. is very small, sin(.DELTA..theta./2) is approximately equal to .DELTA..theta./2, noting that the unit for .DELTA..theta. is the radian, and the following equation (4) is obtained: EQU D=S.multidot..DELTA..theta.. (4)
Next, the wavelength selectivity of the monochromator will be explained. A graph shown in FIG. 12 indicates the relationship between the incidence angle .theta. of X-rays at the point A and the intensity of the diffracted X-rays (i.e., reflected X-rays) therefrom. The abscissa represents the incidence angle .theta. and the ordinate represents the intensity of the diffracted X-rays. With the monochromator having the synthetic multilayered thin film, the half-value width .epsilon. of the diffraction peak observed is about 0.001 radian. If the breadth .DELTA..theta. of the incidence angle .theta. of incident X-rays is more than the half-value width .epsilon., a portion of X-rays, which has an incidence angle out of the half-value width .epsilon., will not satisfy the Bragg equation so as not to contribute to the diffracted intensity.
In the above equation (4), substituting the half-value width .epsilon.=0.001 radian for .DELTA..theta. and 0.5 mm for the focal spot size D leads to that the distance S between the X-ray source and the point A becomes 500 mm. It could be understood that when there is used an X-ray source with an apparent focal spot size of 0.5 mm, the distance S between the X-ray source and the point A should be more than 500 mm for the purpose of narrowing the breadth .DELTA..theta. of the incidence angle .theta. of X-rays at the point A into the above half-value width .epsilon. of the monochromator. If the distance S is less than 500 mm, the breadth .DELTA..theta. of incidence angle, which depends on the X-ray focal spot size, becomes larger than the half-value width .epsilon., so that a portion of the X-rays which are incident on the point A will not satisfy the Bragg equation and will not contribute to the intensity of the diffracted X-rays any longer. Therefore, in FIG. 11, the distance S is required to be more than 500 mm for the purpose of effectively utilizing the intensity of X-rays which are incident on the elliptic monochromator 24. It would be noted further that the minimum distance between the X-ray source 32 and the elliptic monochromator 24 should be more than 500 mm so that the distance S for every point on the reflecting surface of the elliptic monochromator 24 is more than 500 mm.
There will now be discussed the divergence angle .alpha. with which X-rays are caught by the elliptic monochromator 24. As the distance between the X-ray source 32 and the elliptic monochromator 24 increases, the divergence angle .alpha. decreases. As the distance decreases, the divergence angle .alpha. increases. Further, as the divergence angle .alpha. increases, the intensity of the X-rays which are focused by the elliptic monochromator 24 increases. Accordingly, for the purpose of increasing the intensity of the focused X-rays, the distance between the X-ray source 32 and the elliptic monochromator 24 should be smaller. However, for the purpose of narrowing the breadth .DELTA..theta. of incidence angle, which depends on the apparent focal spot size D of the X-ray source, into the half-value width .epsilon. mentioned above, the distance between the X-ray source 32 and the elliptic monochromator 24 should be larger.
After all, even with the use of the elliptic monochromator, there has been the above-described opposite requirements for the purpose of increasing the intensity of the focused X-rays, so that increasing such an intensity has been limited.
Accordingly, an object of the present invention is to provide apparatus for X-ray analysis with which a sample may be irradiated by X-rays of a higher intensity than before in the case of using the elliptic monochromator to focus X-rays on the sample.